# General Relativity stress-energy tensor

## Recommended Posts

I have been trying to grasp the basics of "stress-energy tensor" and most information I have found starts above my head. I hope the basic concept can be put in English words without a ton of complicated math. It seems like more then just mass is being considered in GR when calculating the curvature of spacetime. Is that what it is all about? Links and explanations welcome.

##### Share on other sites

I have been trying to grasp the basics of "stress-energy tensor" and most information I have found starts above my head. I hope the basic concept can be put in English words without a ton of complicated math. It seems like more then just mass is being considered in GR when calculating the curvature of spacetime. Is that what it is all about? Links and explanations welcome.

Sorry about not wanting "complicated" math, but a tensor is a mathematical object. I don't think there's a way around it.

##### Share on other sites

I think I can get you there. This is the representation of mass-energy sources in GR, the right-hand side (RHS) of the equations of non-empty space. Start with the accounting of masses, and since I don't recall at the moment how to write a matrix, look at the 4-vector of velocity distributions defined as: $v^a=<c, v^1,v^2,v^3>$. Simply, the tensor is defined, with mass density field $\rho$, by saying: $T^{ab}=\frac \rho c^2 v^a v^b$. There's more but the sun is out. Later!

##### Share on other sites

Sorry about not wanting "complicated" math, but a tensor is a mathematical object. I don't think there's a way around it.

I do not mind some math (like Norman used) but what I usually get is an equation with a bunch of characters that are not defined plus the goal is also not defined.

Here is what I was looking for to get started but corrections will be needed of course as I do not know the facts or I would not have asked the question.

GR has to do with gravity, but unlike Newton who used only mass, GR will consider things like density and volume to...P=m/v with p=density, m=mass and v=volume....and then we...

See what I am looking for?

The first question is:

What is the stress-energy tensor going to tell us when we do the math? The gravitational attraction of certain matter?

##### Share on other sites

Yes, write out the first two lines of this expressed matrix, where <a,b> range on <0,1,2,3>. Now think about MOMENTUM and ENERGY, and also circulations...

##### Share on other sites

I think I can get you there. This is the representation of mass-energy sources in GR, the right-hand side (RHS) of the equations of non-empty space. Start with the accounting of masses, and since I don't recall at the moment how to write a matrix, look at the 4-vector of velocity distributions defined as: $v^a=<c, v^1,v^2,v^3>$. Simply, the tensor is defined, with mass density field $\rho$, by saying: $T^{ab}=\frac \rho c^2 v^a v^b$. There's more but the sun is out. Later!

Lets make sure I understand each character:

c=speed of light

v=volume and not velocity

$\rho$ = mass density (Different then just mass in KG? how is this determined?)

$T^{ab}$ What does this represent?

##### Share on other sites

'v' is velocity of the mass distribution, 'rho', at some point in the field. We start only accounting for identifiable masses. Then we shall further account for energies and the kitchen sink... $T^{ab}$ is the stress energy tensor, expressed as a 4x4 matrix (rank 2), which is to say how much stress and energy of all types identifiable in our theory, are present here and there. Go one step at a time.

Edited by Norman Albers
##### Share on other sites

'v' is velocity of the mass distribution, 'rho', at some point in the field. We start only accounting for identifiable masses. Then we shall further account for energies and the kitchen sink... $T^{ab}$ is the stress energy tensor, which is to say how much stress and energy of all types identifiable in our theory, are present here and there. Go one step at a time.

The stress energy tensor, $T^{ab}$, is the gravatational attraction of matter considering MOMENTUM and ENERGY, and also circulations... and the kitchen sink.

Am I making progress?

##### Share on other sites

Yes, congratulations! If you write out the first two lines, which is to say let a=0 and run thru the four b's, and then let a=1 and do it again, you will witness momentum and part of the energy. The seemingly excess accounting is needed when we consider any shear force exchanges, and then too in E&M energies where things go in circles. . . . . . .We may have gotten the kitchen sink part right, but how about the cosmic vacuum?¿?¿

Edited by Norman Albers
##### Share on other sites

I knew it could be put into English! Thank you for coming out of your rubber room (compliment) to help me. It is Saturday night and time to chase a little skirt so the "cosmic vacuum" will have to wait.

Thanks Norman

##### Share on other sites

Yo, dude, let coolness reign. I have cut a little oval wood piece in two and do intend to paint nicely on them. One will be hung behind the toilet, maybe neck-high, and will say, "MEN, BANG HEAD HERE". The other will be a foot lower to the side, and will say simply, "WOMEN". What's a riot is having a party to listen<><><> I shall include thick rubber bumpers.

Edited by Norman Albers
Consecutive posts merged.
##### Share on other sites

Have you looked at the Wikipedia article?

In essence it is a collection of functions that describe the energy, momentum, pressure and sheer-stress of "stuff". In general relativity it acts as a source for gravity.

##### Share on other sites

Have you looked at the Wikipedia article?

In essence it is a collection of functions that describe the energy, momentum, pressure and sheer-stress of "stuff". In general relativity it acts as a source for gravity.

Yes I did look at wikipedia but after this thread it makes more sense to me. Thanks for your succinct answer. That is exactly what I was looking for when I started this thread.

## Create an account

Register a new account